Radiative gasdynamics of the nose surface of the Apollo-4 command module at its superobrital reentry

The problem of the radiative gasdynamics of the Apollo-4 command module superorbital entry in the dense terrestrial atmosphere is numerically solved in the two-dimensional formulation of flow past an aerodynamic nose shield on the entry velocity range V_∞ = 10.7?5.75 km/s and the altitude range H = 91.5?35.0 km. The specific regions of the trajectory with strongly nonequilibrium flow in the shock layer, the most high-heat areas of the trajectory, and the regions with strong radiative-gasdynamic interaction in a relatively dense and strongly rarefied oncoming flow are highlighted. The density distributions of the convective and radiative heat fluxes over the body surface are obtained. The spectral composition of the thermal radiation is studied. The results of the calculations are compared and found to be in good agreement with the experimental flight data.     

Radiative heat transfer in absorbing, emitting, and anisotropically scattering boundary-layer flows with reflecting boundary

The heat transfer in absorbing, emitting, and anisotropically scattering boundary-layer flows with reflecting boundary over a flat plate, over a 90-deg wedge, and in stagnation flow is solved by application of the Galerkin method with the particular solution boundary condition I _p (τ₀,ξ,?μ) of the equation of radiative transfer for an inhomogeneous term and the Box method. The exact integral expressions for the radiation part of this problem are developed. The coupling between convective and radiative heat transfer in boundary-layer flows is described by a set of nonlinear simultaneous equations including differential equations and integrodifferential equations. The Galerkin method and the particular solution boundary condition I _p (τ₀,ξ,?μ) are used to analyze the radiation part of the problem. The nonsimilar boundary-layer equations are solved by the Box method. The present numerical procedure solutions are compared in tables with the other exact treating results, the P-3, and P-1 approximation methods for the case of isotropically scattering boundary-layer flows. The effects of linearly anistropically scattering and reflecting surface are taken into account. It is found that the present method is a reliable and efficient numerical procedure and scattering leads to a reduction in the total heat flux. The influence of the forward-backward scattering parameter on the total heat flux decreases with the increase of the surface reflectivity.     

Calculation of Radiation Heat Transfer in Problems of Flow past Bodies with Account for Heat-Shield Coating Mass Loss

Flow past bodies with account for radiation heat transfer near the body nose is considered in connection with the problem of thermal protection of spacecraft entering planetary atmospheres. An approach based on the spherical harmonics method is used for taking radiation into account. The heating and ablation of the heat-shield coating is determined by numerically solving the heat conduction equation with a moving boundary. The thermal problem is solved together with the calculation of the vehicle trajectory, which makes it possible to estimate the effect of the coating mass loss on the trajectory parameters. The approach formulated is realized under the conditions of entry of a spherical segment and a spherically-blunted cone with equal mid-section radii into the Venusian atmosphere. Comparing the results makes it possible to choose the vehicle shape optimal with respect to the thermal regime.     

Numerical analysis of interaction between non-gray radiation and forced convection flow over a recess using the full-spectrum k-distribution method

In the present work, the interaction between non-gray radiation and forced convection in a laminar radiating gas flow over a recess including two backward and forward facing steps in a duct is investigated numerically. Distributions of absorption coefficients across the spectrum (50 cm^?1 < η < 20,000 cm^?1) are obtained from the HITRAN2008 database. The full-spectrum k-distribution method is used to account for non-gray radiation properties, while the gray radiation calculations are carried out using the Planck mean absorption coefficient. To find the divergence of radiative heat flux distribution, the radiative transfer equation is solved by the discrete ordinates method. The effects of radiation–conduction parameter, wall emissivity, scattering coefficient and recess length on heat transfer behaviors of the convection–radiation system are investigated for both gray and non-gray mediums. In addition, the results of gray medium are compared with non-gray results in order to judge if the differences between these two approaches are significant enough to justify the usage of non-gray models. Results show that for air mixture with 10 % CO₂ and 20 % H₂O, use of gray model for the radiative properties may cause significant errors and should be avoided.     

Three-Dimensional Problem of Radiative Gasdynamics of the Apollo-4 Command Module during Superorbital Atmospheric Entry

The three-dimensional problem of radiative gasdynamics of the superorbital entry of the Apollo-4 command module into the dense terrestrial atmosphere at an angle of attack of 25° is numerically solved. The flow conditions corresponding to the flight velocity V_∞ = 10.5 km/s at an altitude H = 67.3 km are considered in detail. The distributions of the densities of convective and radiative heat fluxes along the surface in a flow are obtained. The spectral composition of the thermal radiation attaining the surface is studied. The results of the calculations are successfully compared with the data of two-dimensional calculations.     

Solution to radiative transfer equation in a 3-D rectangular enclosure due to discontinuous heat flow divergence

In this paper a new model and computer code is presented by considering singular and discontinuous heat flow divergence. A hybrid model including Smith’s WSGG model and Coppale and Vervish’s model is used for calculating gas radiative properties. Energy equation is solved simultaneously to reach temperature field which specify gas radiative properties. S ₈ order of discrete ordinate method is used to solve RTE. It is assumed that walls of enclosure are gray, diffuse and opaque with specified temperature. Boundary conditions are corrected in each iteration that change temperature field.     

Experimental modeling of three-dimensional modes of hypersonic flow past cylindrically-blunted bodies

Several sets of experimental studies of the structure of transverse hypersonic flow past blunt bodies (cylinder and truncated wedge) and heat transfer on them are performed in the UT-1M shock tube of the Central Aerohydrodynamics Institute. The purpose of the investigation was to obtain three-dimensional modes of hypersonic flow past the nose surfaces of blunt bodies in an artificially disturbed and nominally uniform flows. The controlled disturbances in the freestream were produced by thin threads pulled over the nozzle exit. In the experiment the flow was visualized using the Töpler method and the heat flux distribution over the cylinder was measured using luminescent temperature transformers. The experiments show that both the flow and the heat transfer in the vicinity of the cylinder nose are very sensitive to vortex disturbances in the oncoming hypersonic flow. In a nominally uniform flow (M_∞ = 8 and Re_∞ = 3160–11670) a steady three-dimensional mode of flow past the nose surface of a blunt wedge could be obtained in the form of a single vortex pair.     

Hypersonic Flow Past the Spherical Nose of a Body in the Presence of a Magnetic Field

The hypersonic flow past the nose of a spherical body containing current sources generating a magnetic field is investigated theoretically and numerically. The magnetohydrodynamic (MHD) flow is analyzed on the basis of the complete system of Navier-Stokes equations containing the force and thermal MHD terms and the electrodynamic equations. Local and integral thermal and aerodynamic characteristics of the body are found. It is shown that the presence of a magnetic field makes it possible to reduce the heat flow to the body in the neighborhood of the stagnation point by several times. However, in this case the total body drag increases.     

Structure and evolution of the airflow generated by a slender body entry near a tube

When a slender body moving forward in open air enters into a confined region, two important unsteady aerodynamic phenomena are generated. An exiting flow is created with a direction opposite to the body movement and inside the confined region, a compression wave is formed. Generation mechanism of compression wave have been extensively studied but so far, no detailed investigation of the exiting flow has ever been reported. The experimental study presented in this paper was undertaken to gain insight into the structure and the evolution of the exit-flow. Experiments were conducted with an axisymmetric apparatus and the explored range of the moving body speed was 5–50 m/s. The study focused on the influence of the body speed and the body nose geometry on the flow. It was shown that the air ejected from the tube entrance generates an annulus jet accompanied by a vortex ring. The vortex development was clarified using laser sheet visualizations associated with unsteady pressure and velocity measurements at the tube entrance. It is constituted by four phases, the pre-vortex phase, the vortex development phase, the vortex convection phase and the vortex breakdown phase. The duration of each of these steps was found to be independent of both the studied parameters in a non-dimensional time scale. Furthermore, neither the body speed nor the nose geometry induced significant changes on the vortex ring evolution, except for extreme conditions (low body speed, V_M.B.<15 m/s, and/or very long nose geometry, L_nose/D_M.B.>6). The evolution of the vortex ring was compared to that of ‘classical’ vortex ring generated at a tube exit by a piston motion with large non-dimensional stroke length. Main similarities and differences were discussed in the paper. In particular, the formation number of vortex ring observed in our experiments was found to be significantly smaller.     

UNSTEADY LIFT AND SOUND PRODUCED BY AN AIRFOIL IN A TURBULENT BOUNDARY LAYER

An analysis is made of the unsteady lift exerted on a stationary rigid body immersed in an incompressible, plane-wall turbulent boundary layer. The lift is expressed as a surface integral over the body involving theupwash velocity induced by the “free” vorticity Ω (found by taking explicit account of the interaction of the body with the flow and excluding the bound vorticity) and a harmonic function X₂that depends only on the shape of the body. The upwash velocity is the free-field velocity given in terms of Ω by the Biot–Savart formula, augmented by the velocity field of a conventional distribution of image vortices in the wall. The function X₂can be interpreted as the velocity potential of flow past the body, produced by motion of the wall at unit speed towards the body. Detailed predictions are made of the lift on a slender airfoil placed in the outer region of the boundary-layer. When the airfoil chord is large compared to the boundary-layer thickness, vortex shedding into the wake causes the magnitude of the net upwash velocity near the trailing edge to be small. The main contributions to the surface integral are then from the nose region, where the upwash velocity may be estimated independently of the fluctuations near the trailing edge. Analytical results for a thin plate airfoil of chord 2a at distance h from the wall show that the lift increases as a/h increases; it is ultimately independent of a and scales with the ratio of h to the hydrodynamic wavelength. Application is made to determine the sound generated by the airfoil in a weakly compressible boundary layer flow over a finite elastic plate.     

Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles

The transient heat transfer behavior in the case of heat removal from a cylindrical heat storage vessel packed with spherical particles was investigated experimentally for various factors (flow rate, diameter of spherical particles packed, temperature difference between flowing cold air and spherical particles accumulating heat, and physical properties of spherical particles). The experiments were covered in ranges of Reynolds number based on the mean diameter of spherical particles packed Re_d = 10.3–2200, porosity?=0.310 to 0.475, ratio of spherical particle diameter to cylinder diameterd/D = 0.0075–0.177 and ratio of length of the cylinder to cylinder diameterL/D=2.5–10. It was found that especially the flow rate and the dimension of spherical particles played an important role in estimating the transient local heat transfer characteristics near the wall of the cylindrical vessel in the present heat storage system. As flow rate and diameter of spherical particles were increased under a given diameter of the cylinder heat storage vessel, the mean heat transfer coefficient between the flow cold air and the hot spherical particles increased and the time period to finish removing heat from the vessel reduced. In addition, the useful experimental correlation equations of mean heat transfer coefficient between both phases and the time period to finish removing heat from the vessel were derived with the functional relationship of Nusselt numberNu _d=f [modified Prandtl numberPr ^* (d/D), Re_d) and Fourier numberFo = f(d/D, L/D, Pr^*, Re_d).     

Self-similar flow of a mixture of a non-ideal gas and small solid particles behind a shock wave in presence of heat conduction, radiation heat flux and a gravitational field

Similarity solutions are obtained for one-dimensional unsteady flow of a dusty gas behind a spherical shock wave with heat conduction and radiation heat flux under a gravitational field of heavy nucleus at the centre (Roche model). The dusty gas is assumed to be a mixture of small solid particles and a non-ideal gas. The equilibrium flow conditions are assumed to be maintained, and the heat conduction is expressed in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient α _R are assumed to vary with temperature and density. In order to obtain similarity solutions the density of the undisturbed medium is assumed to be constant. The effects of an increase in the value of the parameter of non-idealness of the gas in the mixture $\bar{b}$ , the mass concentration of the solid particles in the mixture K _p , the ratio of the density of the solid particles to the initial density of the gas G ₁ and the variation of the heat transfer parameters Γ _R and Γ _c are obtained.     

Radiation-conduction interaction in mixed convection along rotating bodies

This paper investigates the interaction of the steady mixed convection boundary layer flow past a rotating impermeable body placed in a uniform stream moving opposite to the gravitational force and parallel to the axes of the body of revolution with uniform surface temperature and thermal radiation. The fluid considered here is a gray, absorbing-emitting but non-scattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the analysis. The difficulty of having a unified mathematical treatment of this problem is due to the nonsimilarity nature of the governing equations arising from the buoyant force-field and the transverse curvature of the bodies. The important parameters of this problem are the radiation-conduction parameter R _d and the wall to free stream temperature ratio θ _w , for the case of a heated surface. Numerical simulations of the boundary layer equations are performed using the local nonsimilarity method as well as an implicit finite-difference method. The theory is applied to a rotating sphere for the gases with Prandtl number of 0.7. The results are shown graphically in terms of the local skin-friction coefficients and the local rate of heat transfer. Effects of the pertinent parameters R _d and θ _w are also shown on the components of the velocity distribution as well as on the temperature distribution in the boundary layer. Received on 14 January 1997     

Calculation of inviscid radiating gas flow past a blunt body

During hypersonic gas flow past a blunt body with a velocity on the order of the escape velocity or more, the gas radiation in the disturbed region behind the shock wave becomes the primary mechanism for aerodynamic heating and has a significant effect on the distribution of the gasdynamic parameters in the shock layer. This problem has been considered from different points of view by many authors. A rather complete review of these studies is presented in [1–4].In earlier studies [5, 6] the approximation of bulk emission was used. In this approximation, in order to account for the effect of radiative heat transfer a term is added in the energy equation which is equivalent to the body efflux, whose magnitude depends on the local thermodynamic state of the gas. However, the use of this assumption to solve the problem of inviscid flow past a blunt body leads to a singularity at the body [7, 8]. To eliminate the singularity, account is taken of the radiation absorption in a narrow wall layer [7], or the concept of a viscous and heat-conductive shock layer is used [8]. A further refinement was obtained by Rumynskii, who considered radiation selectivity and studied the flow of a radiating and absorbing gas in the vicinity of the forward stagnation point of a blunt body.In the present paper we study the distribution of the gasdynamic parameters in the shock layer over the entire frontal surface of a blunt body in a hypersonic flow of a radiating and absorbing gas with account for radiation selectivity.     

Some physical aspects of radiative and convective heat transfer in the case of nonself-similar blowing on a plate

Heat shielding by blowing has been fairly fully studied in the neighborhood of the stagnation point of a body in a stream [1–3], but for other flow regions the investigation has barely begun [4]. It has been found that the influence of blowing on the radiative and convective fluxes and the influence of radiation on the convection on the side wall can be very different from what is obtained for the flow conditions at the stagnation point. The present paper is a study of the radiative and convective heat transfer on a plate in a H₂ + He stream for constant and self-similar blowing of carbon vapor in the form of C, C₂, and C₃.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 28–35, January–February, 1981.     

Choice of optimal blunting radius of axisymmetric body with account for surface radiation

We consider the problem of determining the optimal blunting with respect to heat transfer of an axisymmetric body in supersonic gas flow at zero angle of attack with account for body surface radiation. Results are presented of a calculation of the optimal blunting radius of a cone with half-angle 10° for various values of the ratio of convective heat flux at the stagnation point to the radiative heat flux. It is shown that for small values of this ratio the small bluntings are optimal.     

Effects of surface radiation on natural convection in a rayleigh-benard square enclosure: steady and unsteady conditions

Coupled laminar natural convection with radiation in air-filled square enclosure heated from below and cooled from above is studied numerically for a wide variety of radiative boundary conditions at the sidewalls. A numerical model based on the finite difference method was used for the solution of mass, momentum and energy equations. The surface-to-surface method was used to calculate the radiative heat transfer. Simulations were performed for two values of the emissivities of the active and insulated walls (ɛ₁=0.05 or 0.85, ɛ₂=0.05 or 0.85) and Rayleigh numbers ranging from 10³ to 2.3×10⁶ . The influence of those parameters on the flow and temperature patterns and heat transfer rates are analyzed and discussed for different steady-state solutions. The existing ranges of these solutions are reported for the four different cases considered. It is founded that, for a fixed Ra, the global heat transfer across the enclosure depends only on the magnitude of the emissivity of the active walls. The oscillatory behavior, characterizing the unsteady-state solutions during the transitions from bicellular flows to the unicellular flow are observed and discussed.     

Heat and mass transfer study of impinging turbulent premixed flames

 Impinging jet combusting flows on granite plates are studied. A mathematical model for calculating heat release in turbulent impinging premixed flames is developed. The combustion including radiative heat transfer and local extinction effects, and flow characteristics are modeled using a finite volume computational approach. Two different eddy viscosity turbulence models, namely the standard k–ɛ and the RNG k–ɛ model with and without radiation (discrete transfer model) are assessed. The heat released predictions are compared with experimental data and the agreement is satisfactory only when both radiative heat transfer and local extinction modeling are taken into account. The results indicate that the main effect of radiation is the decrease of temperature values near the jet stagnation point and along the plate surface. Radiation increases temperature gradients and affects predicted turbulence levels independently of the closure model used. Also, the RNG k–ɛ predicts higher temperatures close the solid plate, with and without radiative heat transfer. Received on 13 November 2000 / Published online: 29 November 2001     

Computational study of combined effects of conduction-radiation and hydromagnetics on natural convection flow past magnetized permeable plate

The computational study of the combined effects of radiation and hydromagnetics on the natural convection flow of a viscous,incompressible,and electrically conducting fluid past a magnetized permeable vertical plate is presented.The governing non-similar equations are numerically solved by using a finite difference method for all values of the suction parameter ξ and the asymptotic solution for small and large values of ξ.The effects of varying the Prandtl number P r,the magnetic Prandtl number P r m,the magnetic force parameter S,the radiation parameter R d,and the surface temperature θ w on the coefficients of the skin friction,the rate of heat transfer,and the current density are shown graphically and in tables.An attempt is made to examine the effects of the above mentioned physical parameters on the velocity profile,the temperature distribution,and the transverse component of the magnetic field.     

Study on laminar film condensation of saturated steam on a vertical flat plate for consideration of various physical factors including variable thermophysical properties

The extended theory of the steady state laminar film condensation process of pure saturated vapour at atmospheric pressure on an isothermal vertical flat plate is established. Its equations provide a complete account of the physical process for consideration of various physical factors including variable thermophysical properties, except for surface tension at the liquid-vapour film interface. First, similarity considerations are proposed to transform the governing system of partial differential equations and its boundary conditions into the corresponding dimensionless system. Then, the dimensionless new system is computed numerically in two steps: First neglecting shear force at the interface, so that the initial values of the boundary conditionsW _{xl, s} andW _{yl, s} are obtained. Then, the calculations of a problem of the three-point boundary-value for coupling the equations of liquid film with those of vapour film are carried out. Furthermore, the correlations for heat transfer coefficient and mass flow rate are proposed by analysis of heat and mass transfer and it is found that the heat transfer coefficient is function of dimensionless temperature gradient $\dot L$ , and that the condensate mass flow rate is function of the mass flow rate parameter (η _lδ W _{xl, s} ? 4W _{yl, s} )of liquid. In addition, the corresponding heat and mass transfer correlations expressed by subcooled temperature Δt are developed. According to Nusselt's theory four different assumptions are set up for an investigation of the effects of the film condensation of saturated vapour, so that the validity of Nusselt's theory can be further clarified. Quantitative comparisons from the results of the heat transfer coefficient and mass flow rate of the condensate indicate that the effect of variable thermophysical properties on the heat and mass transfer is appreciable. The effect of thermal convection in the condensate film is obviously larger than those of shear force at liquid-vapour interface, and the effect of the inertia in the condensate film is very small. Finally, it is also shown that Nusselt's theory, in using Drew reference temperature, will decrease the heat transfer coefficient by at most 5.11%, and will increase the mass flow rate of the condensate by at most 2.45%, provided that the effect of the surface tension is not taken into account.